We introduce new methods of analysing time to event data via extended
versions of the proportional hazards and accelerated failure time (AFT) models.
In many time to event studies, the time of first observation is arbitrary, in
the sense that no risk modifying event occurs. This is particularly common in
epidemiological studies. We show formally that, in these situations, it is not
sensible to take the first observation as the time origin, either in AFT or
proportional hazards type models. Instead, we advocate using age of the subject
as the time scale.
We develop a simulation tool to support policy-decisions about healthcare for
chronic diseases in defined populations. Incident disease-cases are generated
in-silico from an age-sex characterised general population using standard
epidemiological approaches. A novel disease-treatment model then simulates
continuous life courses for each patient using discrete event simulation.
Ideally, the discrete event simulation model would be inferred from complete
longitudinal healthcare data via a likelihood or Bayesian approach.